Cremona's table of elliptic curves

50400 = 2⁵ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	50400dh	Isogeny class
Conductor	50400	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	98304	Modular degree for the optimal curve
Δ	72335025000000 = 26 · 310 · 58 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-11325,218500]	[a1,a2,a3,a4,a6]
Generators	[-105:500:1]	Generators of the group modulo torsion
j	220348864/99225	j-invariant
L	5.1598902348513	L(r)(E,1)/r!
Ω	0.5517150820841	Real period
R	2.3381136398069	Regulator
r	1	Rank of the group of rational points
S	1.0000000000037	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	50400bm1 100800dz2 16800p1 10080u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400dh1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	+	+	-4	2	-2	0	0	-6	8	-2	6	-4	0	-6	-8	-2	-4	4	10	12	4	6	2

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Quadratic twists for elliptic curve 50400dh1

-4	8	-3	5
50400bm1	100800dz2	16800p1	10080u1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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